Answer: 3t + 5 = 32 and 3t+ 2 = 20
Explanation:
We know that someone eats 3 meals per day.
Then if we define the variable t, as the number of days passed since we started counting, we can write the total number of meals eaten as:
M(t) = 3*t
With that in mind, we only can have multiples of 3 (and the coefficient must be 3)
Then the options that remain are:
1) 3*t + 5 = 32
2) 4 - 3*t = 6
3) 3*t + 2 = 20.
Now, let's go to our linear equation:
M(t) = 3*t
As t can only take whole numbers, we can see that M(t) can only be a multiple of 3.
Then we must have:
3*t = multiple of 3.
So let's see our options:
1) 3*t + 5 = 32
3*t = 32 - 5 = 27
27 is a multiple of 3, such that 3*9 = 27, this means that in 9 days, this person would eat 27 meals, then this equation can represent our situation.
2) 4 - 3*t = 6
3*t = 4 - 6 = -2
3*t = -2
-2 is not a multiple of 3 and is a negative number, so this does not make any sense with our initial situation.
3) 3*t + 2 = 20
3*t = 20 - 2 = 18
3*t = 18
18 is a multiple of 3, such that 3*6 = 18
This says that in 6 days, this person would eat 18 meals, then this equation can represent the situation of this problem.